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-   -   How to? Extra term in k-e equation. Implicit-Explicit (https://www.cfd-online.com/Forums/openfoam-programming-development/114679-how-extra-term-k-e-equation-implicit-explicit.html)

 be_inspired March 15, 2013 08:48

How to? Extra term in k-e equation. Implicit-Explicit

Hi all,

I am trying to implement a canopy model into OF.
With respect to the momentum equation, I am seeing several post where the code was similar to the following one:
Quote:
 // Solve the Momentum equation UEqn() == -fvc::grad(p)-fvm::Sp(mag(fvc::Sp(Cd*canopydensity*canopyleaf,U) ),U)
The point is when I need to implement the extra terms in k and epsilon equation.
I have introduced the following ones:
Quote:
 // Turbulent kinetic energy equation volScalarField Fk=0.8*canopydensity_*canopyleaf_*mag(U_)*mag(U_)* mag(U_); tmp kEqn ( fvm::ddt(k_) + fvm::div(phi_, k_) + fvm::SuSp(-fvc::div(phi_), k_) - fvm::laplacian(DkEff(), k_) == G - fvm::Sp(epsilon_/k_, k_) + Fk // Dissipation equation volScalarField Fe=(epsilon_/k_)*Cpepsilon1_*Fk; tmp epsEqn ( fvm::ddt(epsilon_) + fvm::div(phi_, epsilon_) + fvm::SuSp(-fvc::div(phi_), epsilon_) - fvm::laplacian(DepsilonEff(), epsilon_) == C1_*G*epsilon_/k_ - fvm::Sp(C2_*epsilon_/k_, epsilon_) + Fe
It compiles correctly and I obtain some physical results, but I have just found a master thesis where:

Quote:
 // Dissipation equation tmp epsEqn ( fvm::ddt(epsilon_) + fvm::div(phi_, epsilon_) - fvm::Sp(fvc::div(phi_), epsilon_) - fvm::laplacian(DepsilonEff(), epsilon_) == C1_*G*epsilon_/k_ - fvm::Sp(C2_*epsilon_/k_, epsilon_) + fvm::Sp(Cd_*alphaL_/k_*(CEps4_*betap_*pow(mag(U_),3)-CEps5_*betad_*k_*mag(U_)), epsilon_); //Source Term) // Turbulent kinetic energy equation tmp kEqn ( fvm::ddt(k_) + fvm::div(phi_, k_) - fvm::Sp(fvc::div(phi_), k_) - fvm::laplacian(DkEff(), k_) == G - fvm::Sp(epsilon_/k_, k_) + fvm::Sp(Cd_*alphaL_/k_*(betap_*pow(mag(U_),3)-betad_*k_*mag(U_)), k_); //Source term)
The question are:

Is correct my implementation?

what is the advantages to take the extra terms as implicit in the k and epsilon equation with respect to take them as explicit terms? Quick Convergence? Stability?

Thank you very much for your time.

 be_inspired March 19, 2013 11:50

Ok, It seems according to the other topic that it is related to the stability of the equations...

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